Cure 3 = Everyone must be healed up to full because heavy damage AoE is coming soon in the next 5 seconds.
Best Example (Final phase of turn 8, 2x tower burst + possible Allagan Field damage, for a total of three extremely high AoE damage hits over a span of 20 seconds.)

Medica 2 = Boss just used a heavy AoE and goes back to smacking the MT with no follow up AoE attacks.
Example (Pretty much everything pre 2.2)

Disclaimer : Medica 2 usage described above is for when dealing with competent players, as it is assumed competent players will be able to dodge avoidable AoEs that may come after a heavy unavoidable AoE damage (IE: Garuda's feathers, Titan's WotL, Ifrit's plumes).